Related papers: Algebraic Smooth Occluding Contours
This paper contains an attempt to formulate rigorously and to check predictions in enumerative geometry of curves following from Mirror Symmetry. The main tool is a new notion of stable map. We give an outline of a contsruction of…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite…
We identify occlusion reasoning as a fundamental yet overlooked aspect for 3D layout-conditioned generation. It is essential for synthesizing partially occluded objects with depth-consistent geometry and scale. While existing methods can…
This paper presents a novel implicit representation of solid models. With this representation, every solid model can be effectively presented by three layered depth-normal images (LDNIs) that are perpendicular to three orthogonal axes…
Recently, deep learning-based 3D face reconstruction methods have demonstrated promising advancements in terms of quality and efficiency. Nevertheless, these techniques face challenges in effectively handling occluded scenes and fail to…
Neural surfaces (e.g., neural map encoding, deep implicits and neural radiance fields) have recently gained popularity because of their generic structure (e.g., multi-layer perceptron) and easy integration with modern learning-based setups.…
Contours are salient features for image description, but the detection and localization of boundary contours is still considered a challenging problem. This paper introduces a new tool for edge processing implementing the Gestaltism idea of…
To fully understand the 3D context of a single image, a visual system must be able to segment both the visible and occluded regions of objects, while discerning their occlusion order. Ideally, the system should be able to handle any object…
Surveillance and surveying are two important applications of empirical research. A major part of terrain modelling is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than the standard one. For these forms, it is necessary to…
Humans are excellent at perceiving illusory outlines. We are readily able to complete contours, shapes, scenes, and even unseen objects when provided with images that contain broken fragments of a connected appearance. In vision science,…
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…
These are the substantially expanded notes of the lectures of JK at the summer school "Higher-Dimensional Geometry over Finite Fields" in G\"ottingen, June 2007. The first part gives an overview of the methods. The main new result is the…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
High-quality view synthesis relies on volume rendering, splatting, or surface rendering. While surface rendering is typically the fastest, it struggles to accurately model fuzzy geometry like hair. In turn, alpha-blending techniques excel…
Recently, a method to compute the implicit equation of a parametrized hypersurface has been developed by the authors. We address here some questions related to this method. First, we prove that the degree estimate for the stabilization of…
In large-scale scene reconstruction using 3D Gaussian splatting, it is common to partition the scene into multiple smaller regions and reconstruct them individually. However, existing division methods are occlusion-agnostic, meaning that…